The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential equations (PDEs). These data-intensive workloads are primarily constrained by the memory wall, motivating the exploration of emerging number formats -- such as OFP8 (E4M3 and E5M2), bfloat16, and the tapered-precision posit and takum formats -- as potential alternatives to conventional IEEE 754 floating-point representations. This paper evaluates the accuracy and stability of FFT-based computations across a range of formats, from 8 to 64 bits. Round-trip FFT is applied to a diverse set of images, and short-time Fourier transform (STFT) to audio signals. The results confirm posit arithmetic's strong performance at low precision, with takum following closely behind. Posits show stability issues at higher precisions, while OFP8 formats are unsuitable and bfloat16 underperforms compared to float16 and takum.

翻译：快速傅里叶变换（FFT）是高性能计算中应用最广泛的算法之一，在信号处理的谱分析以及偏微分方程（PDE）的数值求解中具有关键作用。这类数据密集型计算任务主要受限于内存墙，因此推动了新兴数格式——如OFP8（E4M3与E5M2）、bfloat16以及锥形精度posit与takum格式——作为传统IEEE 754浮点数表示法的潜在替代方案的研究。本文评估了基于FFT的计算在8位至64位多种数格式下的精度与稳定性。研究对多样化图像集进行了往返FFT变换，并对音频信号实施了短时傅里叶变换（STFT）。结果表明，posit算术在低精度下表现优异，takum紧随其后。Posit在更高精度下表现出稳定性问题，而OFP8格式不适用，bfloat16相较于float16与takum则表现欠佳。